Question

An investment offers $6,500 per year for 20 years, with the first payment occurring one year from now.

If the required return is 7 percent, what is the value of the investment? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

Present value

$

What would the value be if the payments occurred for 45 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

Present value

$

What would the value be if the payments occurred for 70 years? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

  

Present value

$

  

What would the value be if the payments occurred forever? (Do not round intermediate calculations and round your final answer to 2 decimal places, e.g., 32.16.)

  

Present value

$

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Answer 1

Part A:

PV of Annuity = Cash FLow * [1 - (1+r)^-n ] / r

= $ 6500 * [ 1 - (1+0.07)^-20 ] / 0.07

= $ 6500 * [ 1 - (1.07)^-20 ] / 0.07

= $ 6500 * [ 1 - 0.2584] / 0.07

= $ 6500 * [0.7416] / 0.07

= $ 68,861.09

Part B:

PV of Annuity = Cash FLow * [1 - (1+r)^-n ] / r

= $ 6500 * [ 1 - (1+0.07)^-45 ] / 0.07

= $ 6500 * [ 1 - (1.07)^-45 ] / 0.07

= $ 6500 * [ 1 - 0.0476] / 0.07

= $ 6500 * [0.9524] / 0.07

= $ 88,435.89

Part C:

PV of Annuity = Cash FLow * [1 - (1+r)^-n ] / r

= $ 6500 * [ 1 - (1+0.07)^-70 ] / 0.07

= $ 6500 * [ 1 - (1.07)^-70 ] / 0.07

= $ 6500 * [ 1 - 0.0088] / 0.07

= $ 6500 * [0.9912] / 0.07

= $ 92,042.53

Part D:

PV of Annuity = Cash FLow / r

= $ 6500 / 0.07

= $ 92,857.14